Week 3 hw-summer 2018 - Crime dataset using Principal Component Analysis (PCA) to reduce the number PDF

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Crime dataset using Principal Component Analysis (PCA) to reduce the
number of variables/ predictors and avoid multicollinearity....

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WEEK 3 HOMEWORK INSTRUCTIONS •

• •

Every learner should submit his/her own homework solutions. However, you are allowed to discuss the homework with each other (in fact, I encourage you to form groups and/or use the forums) – but everyone must submit his/her own solution; you may not copy someone else’s solution. The homework will be peer-graded. In analytics modeling, there are often lots of different approaches that work well, and I want you to see not just your own, but also others. The homework grading scale reflects the fact that the primary purpose of homework is learning: Rating 4

3 2 1 0

Meaning All correct (perhaps except a few details) with a deeper solution than expected Most or all correct Not correct, but a reasonable attempt Not correct, insufficient effort Not submitted

Point value (out of 100) 100

90 75 50 0

Question 7.1 Describe a situation or problem from your job, everyday life, current events, etc., for which exponential smoothing would be appropriate. What data would you need? Would you expect the value of α (the first smoothing parameter) to be closer to 0 or 1, and why? Question 7.2 Using the 20 years of daily high temperature data for Atlanta (July through October) from Question 6.2 (file temps.txt), build and use an exponential smoothing model to help make a judgment of whether the unofficial end of summer has gotten later over the 20 years. (Part of the point of this assignment is for you to think about how you might use exponential smoothing to answer this question. Feel free to combine it with other models if you’d like to. There’s certainly more than one reasonable approach.) Note: in R, you can use either HoltWinters (simpler to use) or the smooth package’s es function (harder to use, but more general). If you use es, the Holt-Winters model uses model=”AAM” in the function call (the first and second constants are used “A”dditively, and the third (seasonality) is used “M”ultiplicatively; the documentation doesn’t make that clear). Question 8.1 Describe a situation or problem from your job, everyday life, current events, etc., for which a linear regression model would be appropriate. List some (up to 5) predictors that you might use.

Question 8.2 Using crime data from http://www.statsci.org/data/general/uscrime.txt (file uscrime.txt, description at http://www.statsci.org/data/general/uscrime.html ), use regression (a useful R function is lm or glm) to predict the observed crime rate in a city with the following data: M = 14.0 So = 0 Ed = 10.0 Po1 = 12.0 Po2 = 15.5 LF = 0.640 M.F = 94.0 Pop = 150 NW = 1.1 U1 = 0.120 U2 = 3.6 Wealth = 3200 Ineq = 20.1 Prob = 0.04 Time = 39.0 Show your model (factors used and their coefficients), the software output, and the quality of fit. Note that because there are only 47 data points and 15 predictors, you’ll probably notice some overfitting. We’ll see ways of dealing with this sort of problem later in the course....